First image is an example on how to do this exercise. Table one is a referenceI need help to find the target inventory, T Sam's Cat Hotel operates 52 weeks per year, 6 days per week. It purchases kitty litter for $8.00 per bag. The following information is available about these bags: ≻Demand = 55 bags/week≻Order cost = $70/order≻Annual holding cost = 22 percent of cost≻Desired cycle-service level= 99 percent≻Lead time = 4 week(s) (24 working days)≻Standard deviation of weekly demand = 4 bags≻Current on-hand inventory is 250 bags, with no open orders or backorders. Suppose that Sam's Cat Hotel uses a P system. The average daily demand, d, is 9 bags (55/6), and the standard deviation of daily demand,Standard Deviation of Weekly DemandDays per Week/square root of Days per Week, is 1.633 bags. Refer to the standard normal tablefor z-values.a. What P (in working days) and T should be used to approximate the cost trade-offs of the EOQ?The time between orders, P, should be 5252 days. (Enter your response rounded to the nearest whole number.) The target inventory, T, should be enter your response herebags. (Enter your response rounded to the nearest whole number.) The table displayed on this page represents the total area under the normal curve for a point that is a certain number of Z standard deviations to the right of the mean. This is often referred to as a Z-table.### Explanation of the Table:- **Row Labels (Z):** The row headers indicate the Z-value up to one decimal place. These are whole numbers and one decimal (e.g., 0.0, 0.1, 0.2, etc.). - **Column Labels:** Denote the second decimal place of the Z-value, ranging from 0.00 to 0.09.- **Table Data:** Each cell within the table represents the cumulative probability (area under the curve) for the corresponding Z-value. This means the proportion of data within a standard normal distribution that is below this Z-score.### How to Use the Z-table:1. **Determine the Z-score** for which you want to find the cumulative probability.2. **Locate the Z-value**: - Find the whole number and the first decimal in the far-left column (e.g., 1.3). - Find the second decimal in the top row (e.g., 0.04).3. **Find the Intersection**: - Move across the row of your Z-value and down the column of your second decimal to find the value at the intersection. - This value is the cumulative probability.### Example:For a Z-value of 1.36:- Find 1.3 in the Z column.- Move across to the 0.06 column.- The intersecting value is 0.9131, indicating that approximately 91.31% of the data falls below a Z-score of 1.36 in a standard normal distribution.This table helps in statistical analysis to determine probabilities and is widely used in fields such as psychology, finance, and other sciences. **Petromax Enterprises Inventory Control System**Petromax Enterprises uses a continuous review inventory control system for one of its SKUs. Below is the relevant information for this item. The firm operates 52 weeks in a year. A standard normal table is used for z-values.- **Demand** = 91,000 units/year- **Ordering cost** = $30.00/order- **Holding cost** = $3.00/unit/year- **Average lead time** = 9 weeks- **Standard deviation of weekly demand** = 120 units### a. What is the economic order quantity?The **Economic Order Quantity (EOQ)** is calculated as:\[EOQ = \sqrt{\frac{2DS}{H}}\]where:- $ D $ is the demand in units per year,- $ S $ is the ordering cost,- $ H $ is the inventory holding cost.For this item, the EOQ calculation is:\[EOQ = \sqrt{\frac{2 \times 91,000 \times 30.00}{3.00}} = 1,349 \text{ units}\]### b. What should be the safety stock and reorder point for a 98% service level?To provide this service level, the safety stock is calculated using:\[z\sigma_{dLT}, \text{ where } \sigma_{dLT} = \sigma_d\sqrt{L}\]Given:- The standard deviation of weekly demand, $ \sigma_d $ = 120 units.- Lead time, $ L $ = 9 weeks.- From the standard normal table, the z value for a 98% service level is 2.06.The safety stock calculation:\[2.06 \times 120 \times \sqrt{9} = 742 \text{ units}\]Weekly demand, $ \bar{d} $, is calculated as:\[\bar{d} = \frac{91,000}{52} = 1,750 \text{ units}\]The demand during lead time, $ d_L $, is:\[d_L = 1,750 \times 9 = 15,750 \text{ units}\]Finally, the reorder point is:\[15,750 + 742 = 16,492 \text{ units}

Unit cost c =$8.00 per bag A number of operating weeks = 52 weeks per year, 6 days per week. Weekly…

First image is an example on how to do this exercise. Table one is a reference I need help to find the target inventory, T Sam's Cat Hotel operates 52 weeks per year, 6 days per week. It purchases kitty litter for $8.00 per bag. The following information is available about these bags: ≻Demand = 55 bags/week ≻Order cost = $70/order ≻Annual holding cost = 22 percent of cost ≻Desired cycle-service level= 99 percent ≻Lead time = 4 week(s) (24 working days) ≻Standard deviation of weekly demand = 4 bags ≻Current on-hand inventory is 250 bags, with no open orders or backorders. Suppose that Sam's Cat Hotel uses a P system. The average daily demand, d, is 9 bags (55/6), and the standard deviation of daily demand, Standard Deviation of Weekly DemandDays per Week/square root of Days per Week, is 1.633 bags. Refer to the standard normal table for z-values. a. What P (in working days) and T should be used to approximate the cost trade-offs of the EOQ? The time between orders, P, should be 5252 days. (Enter your response rounded to the nearest whole number.) The target inventory, T, should be enter your response here bags. (Enter your response rounded to the nearest whole number.)

6th Edition

ISBN:9781337406659

Author:WINSTON, Wayne L.

Publisher:WINSTON, Wayne L.

Chapter2: Introduction To Spreadsheet Modeling

Section: Chapter Questions

Problem 20P: Julie James is opening a lemonade stand. She believes the fixed cost per week of running the stand...